A lithium secondary battery has rapidly spread recently because of excellent cycle properties. As the electrode active material, particularly the negative electrode active material, of a lithium secondary battery, a lithium-titanium composite oxide having high energy density and excellent in rate characteristics has spread, and on the other hand, a hydrogen titanate compound having high discharge potential and excellent in safety also attracts attention. There are known techniques of using, for example, a spinel-type lithium titanate of Li4Ti5O12 (Patent Literature 1), a ramsdellite-type lithium titanate of Li2Ti3O7 (Patent Literature 2), a lithium titanate of Li2Ti12O25 (Patent Literature 3), a hydrogen titanate compound of H2Ti12O25 (Patent Literature 4), a bronze-type titanium dioxide (Non Patent Literature 1), and the like, as an electrode active material. There is also known a technique of coating a surface of the spinel-type or ramsdellite-type lithium titanate with a cuprate such as copper oxide thereby reduce the decomposition of an electrolyte solution to suppress generation of a gas (Patent Literature 5).